Book Image

Mathematics for Game Programming and Computer Graphics

By : Penny de Byl
5 (1)
Book Image

Mathematics for Game Programming and Computer Graphics

5 (1)
By: Penny de Byl

Overview of this book

Mathematics is an essential skill when it comes to graphics and game development, particularly if you want to understand the generation of real-time computer graphics and the manipulation of objects and environments in a detailed way. Python, together with Pygame and PyOpenGL, provides you with the opportunity to explore these features under the hood, revealing how computers generate and manipulate 3D environments. Mathematics for Game Programming and Computer Graphics is an exhaustive guide to getting “back to the basics” of mathematics, using a series of problem-based, practical exercises to explore ideas around drawing graphic lines and shapes, applying vectors and vertices, constructing and rendering meshes, and working with vertex shaders. By leveraging Python, Pygame, and PyOpenGL, you’ll be able to create your own mathematics-based engine and API that will be used throughout to build applications. By the end of this graphics focussed book, you’ll have gained a thorough understanding of how essential mathematics is for creating, rendering, and manipulating 3D virtual environments and know the secrets behind today’s top graphics and game engines.
Table of Contents (26 chapters)
1
Part 1 – Essential Tools
9
Part 2 – Essential Trigonometry
14
Part 3 – Essential Transformations
20
Part 4 – Essential Rendering Techniques

Processing pixel by pixel

Shaders are run on the GPU in parallel. GPUs require a different type of coding and therefore are written in a different language. We will be using the OpenGL Shader Language (GLSL), which looks very much like C/C++. For the specifications, see https://www.khronos.org/opengl/wiki/OpenGL_Shading_Language.

We will be creating a shader to process vertices and a shader to process fragments. Together, these will replace all the OpenGL drawing operations we’ve used to date. This will give you a chance to explore the movement of mathematical operations from the CPU to the GPU while at the same time understanding how mathematics principles transcend the graphics environment in which they are applied.

The first shader type we will explore is the vertex shader. This code processes one vertex at a time while running multiple versions of itself in parallel, each processing a different vertex. The simplest vertex shader that can be written is one that can...